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On Some Riesz and Carleman Type Inequalities for Harmonic Functions in the Unit Disk

On Some Riesz and Carleman Type Inequalities for Harmonic Functions in the Unit Disk We prove some isoperimetric type inequalities for real harmonic functions in the unit disk belonging to the Hardy space $$h^p$$ h p , $$p>1$$ p > 1 , and for complex harmonic functions in $$h^4$$ h 4 . The results extend some recent results in the area. Further, we discuss some Riesz type results for holomorphic functions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

On Some Riesz and Carleman Type Inequalities for Harmonic Functions in the Unit Disk

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-017-0226-y
Publisher site
See Article on Publisher Site

Abstract

We prove some isoperimetric type inequalities for real harmonic functions in the unit disk belonging to the Hardy space $$h^p$$ h p , $$p>1$$ p > 1 , and for complex harmonic functions in $$h^4$$ h 4 . The results extend some recent results in the area. Further, we discuss some Riesz type results for holomorphic functions.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Dec 4, 2017

References